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How to design a flyback transformer
The transformer for a flyback converter is used as the converters inductor as well as an isolation transformer. =Variables and acronyms= *Universal constants ** Permittivity of free space \mu_o (Wb A−1 m−1) *** \mu_o = 4\pi 10^{-7} (Wb A−1 m−1) *Wire variables: ** \rho , Wire resistivity (Ω-cm) ** I_{tot} , Total RMS winding currents (A) ** I_{m,max} , Peak magnetizing current (A) ** I_{RMS} , Max RMS current, worst case (A) ** P_{cm} , Allowed copper loss (W) ** A_c , Cross sectional area of wire (cm2) *Xformer/inductor design parameters ** n_1, n_2 , turns (turns) ** L_m , Magnetizing inductance (for an xformer) (H) ** L , Inductance (H) ** K_u , Winding fill factor (unitless) ** B_{max} , Core maximum flux density (T) *Core parameters ** EC35, PQ 20/16, 704, etc, Core type (mm) ** K_g , Geometrical constant (cm5) ** K_{gfe} , Geometrical constant (cmx) ** A_c , Cross-sectional area (cm2) ** W_A , Window area (cm2) ** MLT , Mean length per turn (cm) ** l_m , Magnetic path length (cm) ** l , or l_g , Air gap length (cm) ** \mu , Permittivity (Wb A−1 m−1) ** \mu_r , Relative Permittivity (unitless) *** \mu = \mu_o \mu_r ;Acronyms *RMS: root-mean-squared - x_\text{rms} = \sqrt{ \langle x^2 \rangle} \,\! (where \langle \ldots \rangle denotes the arithmetic mean) *MLT: mean length turn *AWG: American wire gauge =Initial calculations= ;Variables * V_o - output voltage V * V_{in} - input voltage V * V_D - diode voltage drop V * V_{Rds} - transistor on voltage V * N - turns ratio unitless * D - duty cycle unitless ;Calculate turns ratio \frac{ V_o + V_D }{ V_{in} - V_{Rds} } = \frac{ 1 }{ N } * \left ( \frac{ D_{max} }{ 1 - D_{max} } \right ) * Diode ** Rectifier: V_D = 0.8V ** Schottky diode: V_D = ? =Inductance calculations= The inductance of the transformer, L_m , controls the current ripple. Say you want a current ripple 50% of average current. \Delta i = 0.5 * I ;Solve for L_m : let n = \frac{n_2}{n_1} I=\frac{n}{D'}I_{load} \Delta i = \frac{nI_{load}}{2D'} L_m = \frac{V_g D T_s}{2 \Delta i} L_m=\frac{\mu A_c n_1^2}{l} The permittivity of free-space is so much larger than the permittivity the transformer material, that the magnetic path length, l , can be estimated to be the air gap length, l_g . so l = l_g and L_m=\frac{\mu_o A_c n_1^2}{l_g} ;Solve for n : Minimize total power loss: P_{tot} = P_{fe} + P_{cu} Core loss: P_{fe} = K_{fe} \Delta B^\beta A_c l_m B_{ac} = \frac{L_m \Delta i}{n_1 A_c} The \beta and K_{fe} are in the core material's datasheets =Core calculations= Core selection ;Variables * P_{Fe} - power loss in the core [ W ] * B_{sat} - saturation flux density [ T ] * B_{max} - max flux density [ T ] * \Delta B - change in flux density [ T ], aka B_{ac} * A_w - winding area [ cm^2 ] * A_e - effective cross-setional area of the core [ cm^2 ] * AP - Area Product [ cm^4 ] * K_u - window utilization factor, or fill factor unitless * N_P - number of turns on the primary unitless * N_S - number of turns on the secondary unitless * N_B - number of turns on the bias unitless * \mu_o - permittivity of free space (air) \mu_o = 2 \pi 10^{-7} H/m ;Material specifications ;Calculate minimal AP needed AP_{min} = 10^3 * \left ( \frac{ L_p * I_{Prms} }{ \Delta T^{ \frac{1}{2} } * K_u * B_{max} } \right )^{1.316} [ cm^4 ] * B_{max} should be less than B_{sat} , to avoid core saturation. for example B_{sat} > 0.3T , then for a conservative calculation use B_{max} = 0.25T * \Delta T = T_{max} - T_{amb} *:Generally T_{max} = 100C and T_{amb}=30C *Using K_u=0.3 for off-line power supplies is a good estimate ;Calculate minimum number of primary and secondary turns * N_{P-min} = \frac{ L_p * I_{pk} * 10^4 }{ B_{max} * A_e } * N_{S-min} = \frac{ N_{P-min} }{ N } ;Calculate actual number of turn on the primary and secondary to be used. * N_S : Round up N_{S-min} to the nearest integer * N_P = N * N_S ;Calculate air gap l_g = \frac{ \mu_o * N_P^2 * A_e * 10^{-2} }{ L_p } =Current calculations= ;Variables * I_{pk} - Ripple current max peak * I_{min} - Ripple current min peak * \Delta I_{pp} - pk-pk ripple current I_{pk} - I_{min} ;Peak current I_{pk} = \left ( \frac{ I_{out-max} }{ N } \right ) * \left ( \frac{ 1 }{ 1 - D_{max} } \right ) + \frac{ \Delta I_L }{ 2 } ;DC current I_{dc}=D \frac{I_{pk}+I_{min}}{2} ;RMS current I_{rms}=\sqrt{ D \left ((I_{pk}+I_{min}) + \frac{1}{3} (I_{pk}+I_{min})^2 \right )} ;AC current I_{rms}=\sqrt{ I_{rms}^2 - I_{dc}^2 } =Power Loss= P_{tot}=P_{fe}+P_{cu} =References= * U of Colorado - Flyback transformer design * TI - "Magnetics Design 4 - Power Transformer Design" - very good, long, description of transformers and design * TDK ferrite materials * IRF - Flyback Transformer Design - nice description of howto wind the transformer * TI - Magnetics Design 5 - Inductor and Flyback Transformer Design - describes various converters DCM and CCM * OFFLINE FLYBACK CONVERTERS DESIGN METHODOLOGY WITH THE L6590 FAMILY - very good, full description of designing an offline flyback converter * Isolated 50 Watt Flyback Converter Using the UCC3809 * TOPSwitch Flyback Transformer Construction Guide Category:Electronics Category:Howto